Effects of faster then light travel on time dilation

[Endercreeper01]

In special relativity, nothing is able to travel faster then the speed of light.

However, if we imagined something traveled faster then light, strange consequences arise.

For example, in special relativity, time is dilated by a factor of

[latex]\frac{d\tau }{dt}=\sqrt{1-\frac{v^2}{c^2}}[/latex]

When the velocity is greater then the speed of light, the time dilation factor becomes imaginary. What exactly would it mean if the time dilation factor was imaginary? What would be observed by a stationary observer if an object did travel faster then light?

[swansont]

The equations that tell us nothing can travel faster than c might not be valid for things that travel faster than c. You can't use physics to determine the behavior of something that physics says isn't possible.

[Strange]

This might answer some of your questions: https://en.wikipedia.org/wiki/Tachyon

 

Note that there is no evidence for tachyons, and good theoretical reasons to assume they don't exist.

[Janus]

To add to swansont's answer, consider what happens if you try and use Relativistic velocity addition with FTL speeds.

For instance, consider two ships traveling away from a point in opposite directions at 1.5c.

If you apply Relativistic velocity addition to find the speed of the ships relative to each other, you get 0.923c, which is less than the speed at which either ship is moving away from the origin point.

 

But it gets better. If one of the ships than applies the brakes in order to decrease its relative speed with respect to the other ship, the relative speed between ships increases So for instance, if he slowed to 1.4c relative to the origin, the relative velocity between ships increases to 0.935c.

 

The same type of thing happens if a ship at the origin decides to chase after one of the ships. If you start moving towards one of the ships at 0.1c, you will find that the relative speed between you and the ship increases to 1.65c.